Search Results (42)

The stability of a circular vortex is studied in the thermal quasi-geostrophic (TQG) model. Several radial distributions of vorticity and buoyancy (temperature) are considered for the mean flow. First, the linear stability of these vortices is addressed. The linear problem is solved exactly for a simple flow, and two stability criteria are then derived for general mean flows. Then, the growth rate and most unstable wavenumbers of normal-mode perturbations are computed numerically for Gaussian and cubic exponential vortices, both for elliptical and higher mode perturbations. In TQG, contrary to usual QG, short waves can be linearly unstable on shallow vorticity profiles. Linearly, both stratification and bottom topography (under specific conditions) have a stabilizing role. In a second step, we use a numerical model of the nonlinear TQG equations. With a Gaussian vortex, we show the growth of small-scale perturbations during the vortex instability, as predicted by the linear analysis. In particular, for an unstable vortex with an elliptical perturbation, the final tripolar vortices can have a turbulent peripheral structure, when the ratio of mean buoyancy to mean velocity is large enough. The frontogenetic tendency indicates how small-scale features detach from the vortex core towards its periphery, and thus feed the turbulent peripheral vorticity. We confirm that stratification and topography have a stabilizing influence as shown by the linear theory. Then, by varying the vortex and perturbation characteristics, we classify the various possible nonlinear regimes. The numerical simulations show that the influence of the growing small-scale perturbations is to weaken the peripheral vortices formed by the instability, and by this, to stabilize the whole vortex. A finite radius of deformation and/or bottom topography also stabilize the vortex as predicted by linear theory. An extension of this work to stratified flows is finally recommended. Full article

Due to computational constraints, ocean numerical models are often executed on low-resolution (LR) grids. To maintain consistency between LR simulations and coarsened high-resolution (HR) solutions, a subgrid forcing term is commonly integrated into the LR model as a parameterization scheme. Although numerous data-driven parameterizations have been developed to establish the relationship between resolved LR variables and corresponding subgrid forcing, the accurate extraction of target subgrid forcing remains an open challenge that significantly impacts the performance of such parameterizations. Small-scale dissipation (ssd) operators are widely used to enhance numerical stability while introducing minimal energy dissipation; however, this study demonstrates that these operators critically influence the accurate representation of subgrid forcing: an aspect that has not been adequately addressed. Within a quasi-geostrophic ocean modeling framework, new formulations have been rigorously derived for subgrid forcing that explicitly accounts for ssd effects. Numerical experiments confirm that the proposed forcing enables LR simulations to reproduce coarsened HR results with high fidelity. This work demonstrates that greater attention to the specific numerical discretization scheme is required for the accurate extraction of subgrid forcing from HR simulations. Although these newly developed extraction algorithms are diagnostic in nature, they could provide accurate target data that facilitate the subsequent development of data-driven parameterization schemes. Full article

Inertial instability is a key process in the dynamics of rotating and stratified fluids, which arises when the absolute vorticity of the flow becomes negative. This study explored the nonlinear behavior of inertial instability by incorporating a hidden symmetry into the equations of motion governing atmospheric dynamics. The atmosphere was modeled as a complex system composed of interacting structural elements, each capable of oscillatory motion influenced by planetary rotation and geostrophic shear. By applying a symmetry-based framework rooted in projective geometry and Riccati-type transformations, we show that synchronization and structural coherence can emerge spontaneously, independent of external forcing. This hidden symmetry leads to rich dynamical behavior, including phase coupling, quasi-periodicity, and bifurcations. Our results suggest that inertial instability, beyond its classical linear interpretation, may play a significant role in organizing large-scale atmospheric patterns through internal geometric constraints. Full article

In this paper, we used Fourier Neural Operator (FNO) networks to solve reaction–diffusion equations. The FNO is a novel framework designed to solve partial differential equations by learning mappings between infinite-dimensional functional spaces. We applied the FNO to the Surface Quasi-Geostrophic (SQG) equation, and we tested the model with two significantly different initial conditions: Vortex Initial Conditions and Sinusoidal Initial Conditions. Furthermore, we explored the generalization ability of the model by evaluating its performance when trained on Vortex Initial Conditions and applied to Sinusoidal Initial Conditions. Additionally, we investigated the modes (frequency parameters) used during training, analyzing their impact on the experimental results, and we determined the most suitable modes for this study. Next, we conducted experiments on the number of convolutional layers. The results showed that the performance of the models did not differ significantly when using two, three, or four layers, with the performance of two or three layers even slightly surpassing that of four layers. However, as the number of layers increased to five, the performance improved significantly. Beyond 10 layers, overfitting became evident. Based on these observations, we selected the optimal number of layers to ensure the best model performance. Given the autoregressive nature of the FNO, we also applied it to solve the Gray–Scott (GS) model, analyzing the impact of different input time steps on the performance of the model during recursive solving. The results indicated that the FNO requires sufficient information to capture the long-term evolution of the equations. However, compared to traditional methods, the FNO offers a significant advantage by requiring almost no additional computation time when predicting with new initial conditions. Full article

Ocean circulation plays an important role in the formation and occurrence of extreme climate events. The study shows that the periodic variation of ocean circulation under strong wind stress is closely related to climate oscillation. Ocean circulation is a nonlinear dynamic system, which shows complex nonlinear characteristics, so the essence behind ocean circulation has not been clearly explained. Therefore, the response and evolution of the circulation system to wind stress are studied based on the bifurcation and catastrophe theories in nonlinear dynamics. First, the quasi-geostrophic gyre equation and the normalized gravity model are introduced and developed to study ocean circulation driven by wind stress, and solved using the Galerkin method. Then, the bifurcation and catastrophe behaviors of the system governed by the low-order ocean circulation model during the change in wind stress intensity and the coexistence of multiple equilibria in the circulation system are studied in detail. The results show that saddle and unstable nodes appear in the system after a cusp catastrophe. With the change in model parameters, the unstable node becomes the unstable focus, and then the subcritical Hopf bifurcation occurs. The system forms a bistable interval when the system undergoes a catastrophe twice, and the system shows hysteresis. In addition, multiple equilibrium states are coexisting in the circulating system, and the unstable equilibrium state always changes into a stable equilibrium state through vortex movement. Therefore, there is a route for the system to induce short-term climate oscillation, that is, in the multi-stable equilibrium state of the system, the vortex oscillates after being subject to small disturbances, and then triggers climate oscillation. Full article

Atmospheric gravity waves (GWs) can strongly modulate middle atmospheric circulation and can be a significant factor for the coupling between the lower atmosphere and the middle atmosphere. GWs are difficult to resolve in global atmospheric models due to their small scale; thus, GW observations play an important role in middle atmospheric studies. The climatology of GW variance and momentum in the low-latitude mesosphere and lower thermosphere (MLT) region are revealed using multiple meteor radars, which are located at Kunming (25.6°N, 103.8°E), Sanya (18.4°N, 109.6°E), and Fuke (19.5°N, 109.1°E). The climatology and longitudinal variations in GW momentum fluxes and variance over the low-latitude region are reported. The GWs show strong seasonal variations and can greatly control the mesospheric horizontal winds via modulation of the quasi-geostrophic balance and momentum deposition. The different GW activities between Kunming and Sanya/Fuke are possibly consistent with the unique prevailing surface winds over Kunming and the convective system over the Tibetan Plateau according to the European Centre for Medium-Range Weather Forecasts (ECMWF), Reanalysis v5 (ERA5) data, and outgoing longwave radiation (OLR) data. These findings provide insight for better understanding the coupling between the troposphere and mesosphere. Full article

We present a new explicit quasi-Lagrangian integration scheme with the three-dimensional cubic spline function transform (transform = fitting + interpolation, referred to as the “spline format”) on a spherical quasi-uniform longitude–latitude grid. It is a consistent longitude–latitude grid, and to verify the feasibility, accuracy, convergence, and stability of the spline format interpolation scheme for the upstream point on the longitude–latitude grid, which may map a quasi-uniform longitude–latitude grid, a set of ideal, exact test schemes is adopted, which are recognized and proven to be effective internationally. The equilibrium flow test, cross-polar flow test, and Rossby–Haurwitz wave test are used to illustrate the spline scheme uniformity to the linear scheme and to overcome the over-dense grid in the polar region and the non-singularity of the poles. The cross-polar flow test demonstrates that the geostrophic wind crosses the polar area correctly, including the South Pole and North Pole. A non-hydrostatic, fully compressible dynamic core is used to complete the density flow test, demonstrating the existence of a time-varying reference atmosphere and that the spline format can simulate highly nonlinear fine-scale transient flows. It can be compared for the two results of the density flow test between the solution with the spline format and the benchmark reference solution with the linear format. Based on the findings, the non-hydrostatic dynamic core with the spline format is recommended for adoption. When simulated for the flow over an ideal mountain, through the “topographic gravity wave test”, the bicubic surface terrain and terrain-following height coordinates, time-split integration, and vector discrete decomposition can be derived successfully. These may serve as the foundations for a global, unified spline-format numerical model in the future. Full article

Observational analyses reveal that a dominant mode in the South Asian Monsoon region in boreal summer is a westward-propagating synoptic-scale disturbance with a typical wavelength of 4000 km that is coupled with moistening and precipitation processes. The disturbances exhibit an eastward tilt during their development before reaching their maximum activity center. A 2.5-layer model that extends a classic 2-level quasi-geostrophic model by including a prognostic lower-tropospheric moisture tendency equation and an interactive planetary boundary layer was constructed. The eigenvalue analysis of this model shows that the most unstable mode has a preferred zonal wavelength of 4000 km, a westward phase speed of 6 m s⁻¹, an eastward tilt vertical structure, and a westward shift of maximum moisture/precipitation center relative to the lower-tropospheric vorticity center, all of which agree with the observations. Sensitivity experiments show that the moisture–vortex instability determines, to a large extent, the growth rate, while the baroclinic instability helps set up the preferred zonal scale. Ekman-pumping-induced vertical moisture advection prompts an in-phase component of perturbation moisture relative to the low-level cyclonic center, allowing the generation of available potential energy and perturbation growth, regardless of whether or not a low-level mean westerly is presented. In contrast to a previous study, the growth rate is reversely proportional to the convective adjustment time. The current work sheds light on understanding the moisture–vortex and the baroclinic instability in a monsoonal environment with a pronounced easterly vertical shear. Full article

Several types of spatial symmetry in vortex structures within rotating stratified fluids are examined by looking at self-propagating configurations in the quasigeostrophic model. The role of symmetry breaking in the dynamics of geophysical waves, vortices and instabilities is highlighted. In particular, the energy exchange of the large-scale vertical shear with monopolar and dipolar vortices is analyzed. Various coupled vortex-wave structures are described in terms of wavy and evanescent modes. The Rossby wave radiation is shown to induce a zonal asymmetry, which is needed for the energy support and self-amplification of vortices in large-scale flow. The consequences for the evolution of the most long-lived vortices in the subtropical westward flows are discussed. Full article

In the present paper, we investigate the sea surface height (SSH) anomalies caused by polar lows (PLs) crossing the central part of the Barents Sea and verify if the barotropic response is detectable in the shallow Arctic seas. Analysis of the SSH anomalies in response to the passage of two PLs is performed using satellite altimeter measurements and model simulations. The observed SSH anomalies contained an inverse barometer correction; therefore, they were presumably caused only by the action of surface wind stress in the PLs. The SSH anomalies along the satellite altimeter tracks had the shape of a trough, with the lowest surface height near the center of the PL. The observed anomalies were well distinguished within about one day after the PL passage, with the largest negative value of 0.6 m. The SSH anomalies are analyzed using a simplified model of the ocean barotropic response to the surface wind stress, derived from the hourly wind fields provided in the ERA5 reanalysis dataset. The model quantitatively reproduced the SSH anomalies along most satellite altimeter tracks crossing the PL trajectories. The model simulations revealed that the largest negative SSH anomalies were observed in areas where the PL translation velocity was low and its moving direction changed with the trajectory curvature radius, which was much smaller than the barotropic radius of deformation. The estimated quasi-geostrophic current velocities corresponding to the SSH anomalies in the wakes of the PLs reached 0.15 m/s, which were comparable to the current velocities observed in the Barents Sea. Full article

Macroscale turbulence in the atmosphere is observed to be self-organized into large-scale structures such as zonal jets and robust waves and vortices. A simple model containing the relevant dynamics of turbulence self-organization is quasi-geostrophic turbulence in a stably stratified atmosphere approximated with a single-layer fluid on a beta-plane. Numerical simulations of this model have shown the dominance of Rossby waves, zonal jets and robust vortices in different regions of the parameter space. In this work, we perform numerical integrations of this model and focus on the regime in which robust large-scale vortices dominate the flow. The goal is to identify the Lagrangian coherent vortices that trap the same air masses in their core throughout their life cycle and to obtain their characteristics. The vortices are identified using an objective algorithm based on the Lagrangian-averaged vorticity deviation calculated using the advection of Lagrangian particles by the flow. Long-lived vortices with scales comparable to the deformation scale are found with a symmetry between cyclones and anti-cyclones as expected from the simplified dynamics of the model. The scale as well as the life span of the vortices are also found to increase alongside an increase in the strength of turbulence. Full article

The connection between the heat transfer and characteristic flow velocities of planetary core-style convection remains poorly understood. To address this, we present novel laboratory models of rotating Rayleigh–Bénard convection in which heat and momentum transfer are simultaneously measured. Using water (Prandtl number, $Pr\simeq 6$) and cylindrical containers of diameter-to-height aspect ratios of $\Gamma \simeq 3,1.5,0.75$, the non-dimensional rotation period (Ekman number, E) is varied between ${10}^{-7}\lesssim E\lesssim 3\times {10}^{-5}$ and the non-dimensional convective forcing (Rayleigh number, $Ra$) ranges from ${10}^7\lesssim Ra\lesssim {10}^{12}$. Our heat transfer data agree with those of previous studies and are largely controlled by boundary layer dynamics. We utilize laser Doppler velocimetry (LDV) to obtain experimental point measurements of bulk axial velocities, resulting in estimates of the non-dimensional momentum transfer (Reynolds number, $Re$) with values between $4\times {10}^2\lesssim Re\lesssim 5\times {10}^4$. Behavioral transitions in the velocity data do not exist where transitions in heat transfer behaviors occur, indicating that bulk dynamics are not controlled by the boundary layers of the system. Instead, the LDV data agree well with the diffusion-free Coriolis–Inertia–Archimedian (CIA) scaling over the range of $Ra$ explored. Furthermore, the CIA scaling approximately co-scales with the Viscous–Archimedian–Coriolis (VAC) scaling over the parameter space studied. We explain this observation by demonstrating that the VAC and CIA relations will co-scale when the local Reynolds number in the fluid bulk is of order unity. We conclude that in our experiments and similar laboratory and numerical investigations with $E\gtrsim {10}^{-7}$, $Ra\lesssim {10}^{12}$, $Pr\simeq 7$, heat transfer is controlled by boundary layer physics while quasi-geostrophically turbulent dynamics relevant to core flows robustly exist in the fluid bulk. Full article

Flow configurations that maximize the instantaneous rate of conversion from potential to kinetic energy are sought using a combination of analytical and numerical methods. A hydrostatic model is briefly investigated, but the presence of unrealistic ageostrophic flow configurations renders the results unrealistic. In the quasigeostrophic (QG) model, flow configurations that locally optimize the conversion rate are found, but it remains unclear if these flow configurations produce the global maximum conversion rate. The difficulty is associated with the fact that in the QG model, the vertical velocity is a quadratic function of the QG streamfunction, which renders the conversion rate a cubic function of the QG streamfunction. For these locally maximal conversion rates, the rate of conversion depends on the horizontal length scale of the flow: for scales larger than the deformation radius, the maximal rates are small and decrease as the horizontal scale increases; for scales smaller than the deformation radius, the maximal conversion rate rises until it becomes comparable to the maximal rate at which potential energy can be extracted from the mean flow. Full article

The stability of two superposed buoyancy vortices is studied linearly in a two-level Surface Quasi-Geostrophic (SQG) model. The basic flow is chosen as two circular vortices with uniform buoyancy, coaxial, and the same radius. A perturbation with a single angular mode is added to this mean flow. The SQG equations linearized in perturbation around this basic flow form a two-dimensional ODE for which the normal and singular mode solutions are numerically computed. The instability of these two vortices depends on several parameters. The parameters varied here are: the vertical distance between the two levels and the two values of the vortex buoyancies (called vortex intensity hereafter); the other parameters remain fixed. For normal modes, the system is stable if the levels are sufficiently far from each other vertically, to prevent vertical interactions of the buoyancy patches. Stability is also reached if the layers are close to each other, but if the vortices have very different intensities, again preventing the resonance of Rossby waves around their contours. The system is unstable if the vortex intensities are similar and if the two levels are close to each other. The growth rates of the normal modes increase with the angular wave-number, also corresponding to shorter vertical distances. The growth rates of the singular modes depend more on the distance between the levels than on the ratio of the vortex intensities, at a short time; as expected, they converge towards the growth rates of the normal modes. This study remaining linear does not predict the final evolution of such unstable vortices. This nonlinear evolution will be studied in a sequel of this work. Full article

The mechanism of convection initiation (CI) over Ili River Valley (IRV) in Xinjiang, Northwest China, was investigated based on both weather stations and radar observations and Weather Research and Forecasting (WRF) model simulation. Observations showed that many CIs occurred repeatedly, and most of them underwent significant intensification both in size and intensity, and eventually formed an extreme rainfall-producing mesoscale convective system (MCS) in the IRV. Besides, there was a relatively strong boundary layer westerly jet (BLWJJ, horizontal wind speed exceeding 12 m s⁻¹) along with significant cold advection. The overall features of the CIs and associated MCS are generally well reproduced by the WRF simulation. Simulation results showed that there were some horizontal convective rolls (HCRs) developed ahead of the BLWJ and generated significant convergence (up to ~2 × 10⁻³ s⁻¹) in the low level that further induced intense updraft aloft (vertical velocity exceeding 3.5 m s⁻¹) which finally resulted in the CIs. Further investigations indicated that, as the main contributor to the HCRs, the BLWJ was generated due to the funneling effect when the descending westerlies entered the middle reaches of the IRV. A qualitative analysis based on the quasi-geostrophic omega equation revealed that the descending flow in mid- to lower troposphere in the middle reaches of the IRV was mainly contributed by the vorticity advection, while the descending in the lower troposphere was dominated by both vorticity advection and cold advection. Full article